Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Physical Experiments and Computer Experiments Read chapter Read first chapter

2018 | OriginalPaper | Chapter

7. Sensitivity Analysis and Variable Screening

Authors : Thomas J. Santner, Brian J. Williams, William I. Notz

Published in: The Design and Analysis of Computer Experiments

Publisher: Springer New York

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter discusses sensitivity analysis and the related topic of variable screening. The setup is as follows. A vector of inputs \(\boldsymbol{x} = (x_{1},\ldots,x_{d})\) is given which potentially affects a “response” function \(y(\boldsymbol{x}) = y(x_{1},\ldots,x_{d})\). Sensitivity analysis seeks to quantify how variation in \(y(\boldsymbol{x})\) can be apportioned to the inputs x 1, …, x d and to the interactions among these inputs.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Some Criterion-Based Experimental Designs
next chapter Calibration
Literature
Adler RJ (1990) An introduction to continuity, extrema, and related topics for general Gaussian processes. Institute of Mathematical Statistics, Hayward, CA
Barton RR (1999) Graphical methods for the design of experiments. Lecture notes in statistics, vol 143. Springer, New York, NYCrossRef
Box GE, Draper NR (1987) Empirical model-building and response surfaces. Wiley, New York, NYMATH
Campbell K (2001) Functional sensitivity analysis for computer model output. In: Bodt BA, Wegman EJ (eds) Proceedings of the seventh U.S. army conference on applied statistics. Army Research Laboratory, pp 35–46
Campbell KS, McKay MD, Williams BJ (2006) Sensitivity analysis when model outputs are functions. Reliab Eng Syst Saf 91:1468–472CrossRef
Campolongo F, Cariboni J, Saltelli A (2007) An effective screening design for sensitivity analysis of large models. Environ Model Softw 22:1509–1518CrossRef
Campolongo F, Saltelli A, Cariboni J (2011) From screening to quantitative sensitivity analysis. A unified approach. Comput Phys Commun 43:39–52MATH
Chen W, Jin R, Sudjianto A (2005) Analytical variance-based global sensitivity analysis in simulation-based design under uncertainty. J Mech Des 127:875–876CrossRef
Chen W, Jin R, Sudjianto A (2006) Analytical global sensitivity analysis and uncertainty propogation for robust design. J Qual Technol 38:333–348CrossRef
Constantine PG, Dow E, Wang Q (2014) Active subspace methods in theory and practice: applications to kriging surfaces. SIAM J Sci Comput 36(4):A1500–A1524MathSciNetCrossRef
Davis C (2015) A Bayesian approach to prediction and variable selection using nonstationary Gaussian processes. PhD thesis, Department of Statistics, The Ohio State University, Columbus, OH
Draper NR, Smith H (1981) Applied regression analysis. Wiley, New York, NYMATH
Helton JC, Johnson JD, Sallaberry CJ, Storlie CB (2006) Survey of sampling-based methods for uncertainty and sensitivity analysis. Reliab Eng Syst Saf 91:1175–1209CrossRef
Joseph VR, Hung Y, Sudjianto A (2008) Blind kriging: a new method for developing metamodels. ASME J Mech Des 130:377–381CrossRef
Kleijnen JPC, Bettonvil B, Persson F (2006) Screening for the important factors in large discrete-event simulation models: sequential bifurcation and its applications. In: Dean AM, Lewis SM (eds) Screening: methods for experimentation in industry, drug discovery and genetics. Springer, New York, NY, pp 287–307CrossRef
Lewis SM, Dean AM (2001) Detection of interactions in experiments on large numbers of factors (with discussion). J R Stat Soc Ser B 63:633–672MathSciNetCrossRef
Linkletter C, Bingham D, Hengartner N, Higdon D, Ye KQ (2006) Variable selection for Gaussian process models in computer experiments. Technometrics 48:478–490MathSciNetCrossRef
Loeppky JL, Williams BJ, Moore LM (2013) Global sensitivity analysis for mixture experiments. Technometrics 55:68–78MathSciNetCrossRef
Marrel A, Iooss B, Lauren B, Roustant O (2009) Calculations of Sobol indices for the Gaussian process metamodel. Reliab Eng Syst Saf 94:742–751CrossRef
Montgomery GP, Truss LT (2001) Combining a statistical design of experiments with formability simulations to predict the formability of pockets in sheet metal parts. Technical report 2001-01-1130, Society of Automotive Engineers
Moon H (2010) Design and analysis of computer experiments for screening input variables. PhD thesis, Department of Statistics, The Ohio State University, Columbus, OH
Moon H, Santner TJ, Dean AM (2012) Two-stage sensitivity-based group screening in computer experiments. Technometrics 54(4):376–387MathSciNetCrossRef
Morris MD (1991) Factorial sampling plans for preliminary computational experiments. Technometrics 33:161–174CrossRef
Morris MD (2006) An overview of group factor screening. In: Dean AM, Lewis SM (eds) Screening: methods for experimentation in industry, drug discovery and genetics. Springer, New York, NY, pp 191–206CrossRef
Morris MD, Moore LM, McKay MD (2006) Sampling plans based on balanced incomplete block designs for evaluating the importance of computer model inputs. J Stat Plann Inf 136(9):3203–3220MathSciNetCrossRef
Morris MD, Moore LM, McKay MD (2008) Using orthogonal arrays in the sensitivity analysis of computer models. Technometrics 50(2):205–215MathSciNetCrossRef
Pujol G (2009) Simplex-based screening designs for estimating metamodels. Reliab Eng Syst Saf 94:1156–1160CrossRef
Russi TM (2010) Uncertainty quantification with experimental data and complex system models. PhD thesis, UC Berkeley, CA
Saltelli A (2002) Making best use of model evaluations to compute sensitivity indices. Comput Phys Commun 145 (2):280–297MathSciNetCrossRef
Saltelli A, Sobol´ IM (1995) About the use of rank transformation in sensitivity analysis of model output. Reliab Eng Syst Saf 50:225–239CrossRef
Saltelli A, Chan K, Scott E (2000) Sensitivity analysis. Wiley, ChichesterMATH
Saltelli A, Tarantola S, Campolongo F, Ratto M (2004) Sensitivity analysis in practice: a guide to assessing scientific models. Wiley, ChichesterMATH
Saltelli A, Annoni P, Azzini I, Campolongo F, Ratto M, Tarantola S (2010) Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput Phys Commun 181:259–270MathSciNetCrossRef
Savitsky T, Vannucci M, Sha N (2011) Variable selection for nonparametric Gaussian process priors: models and computational strategies. Stat Sci 26(1):130–149MathSciNetCrossRef
Sobol´ IM (1990) Sensitivity estimates for nonlinear mathematical models. Matematicheskoe Modelirovanie 2:112–118
Sobol´ IM (1993) Sensitivity estimates for nonlinear mathematical models. Math Model Comput Exp 1(4):407–414
Sobol´ I, Kucherenko S (2009) Derivative based global sensitivity measures and their link with global sensitivity indices. Math Comput Simul 79(10):3009–3017MathSciNetCrossRef
Storlie CB, Helton JC (2008) Multiple predictor smoothing methods for sensitivity analysis: description of technique. Reliab Eng Syst Saf 93:28–54CrossRef
Storlie CB, Swiler LP, Helton JC, Salaberry CJ (2009) Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models. Reliab Eng Syst Saf 94(11):1735–1763CrossRef
Sun F, Santner TJ, Dean AM (2013) One-at-a-time designs for estimating elementary effects of simulator experiments with non-rectangular input regions. Stat Appl 11:15–32
Svenson JD (2011) Computer experiments: multiobjective optimization and sensitivity analysis. PhD thesis, Department of Statistics, The Ohio State University, Columbus, OH
Svenson J, Santner TJ, Dean A, Moon H (2014) Estimating sensitivity indices based on Gaussian process metamodels with compactly supported correlation functions. J Stat Plann Inf 144:160–172MathSciNetCrossRef
Van Der Vaart AW (1998) Asymptotic statistics. Cambridge University Press, CambridgeCrossRef
Vine AE, Lewis SM, Dean AM (2005) Two-stage group screening in the presence of noise factors and unequal probabilities of active effects. Stat Sinica 15:871–888MathSciNetMATH
Welch WJ, Buck RJ, Sacks J, Wynn HP, Mitchell TJ, Morris MD (1992) Screening, predicting, and computer experiments. Technometrics 34:15–25CrossRef
Yaglom AM (1962) Introduction to the theory of stationary random functions. Dover, New York, NYMATH
Metadata
Title
Sensitivity Analysis and Variable Screening
Authors
Thomas J. Santner
Brian J. Williams
William I. Notz
Copyright Year
2018
Publisher
Springer New York
Book
The Design and Analysis of Computer Experiments

Print ISBN: 978-1-4939-8845-7

Electronic ISBN: 978-1-4939-8847-1

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-1-4939-8847-1_7

Premium Partner

    Image Credits